Reflection and refraction of SH‐waves at a corrugated interface between two monoclinic elastic half‐spaces

A problem of reflection and transmission of shear wave incident upon a corrugated interface between two monoclinic solid half‐spaces have been investigated. Rayleigh's method of approximation is used to investigate the reflection and transmission coefficients for first and second approximation of the corrugation. For a special interface, closed‐form expressions of these coefficients for the first order approximation of the corrugation are obtained. It is found that these coefficients are functions of amplitude of corrugation, elastic parameters of the media, frequency of the incident wave and angle of incidence. The numerical computations are performed for a specific model and the results obtained are presented graphically. It is found that the reflection and transmission coefficients are strongly influenced by the corrugation and the elastic properties of the media. Results of some earlier workers in this field have been reduced as particular case from the present formulation. Copyright © 2004 John Wiley & Sons, Ltd.     

Observations on the Abiotic Factors and Planktonic Periodicity in a Shallow Pond of the Highlands of Shillong (India)

The pond, situated at an altitude of 4862 m, shows an annual variation of temperature between 15 and 27 °C in a close correlation with the air temperature. In the case of a weakly acidic reaction of water an inverse relation exists between pH and conductivity and between free CO₂ and alkalinity. The nutrient content of 0.05 mg/l PO₄-P and NO₃-N each is low, the phosphorus concentration being maintained by re-solution from the sediment. Chlorophyceae and diatoms are dominant in the phytoplankton alternately, and rotatoria and copepoda are dominant in the zoo-plankton in winter and in summer, respectively. The pronounced changes in the composition of plankton do not show any definite dependence on the physico-chemical factors, particularly since a significant share of the nutrient metabolism and the oxygen balance in the pond investigated is determined by macrophytes.     

Robe’s restricted problem of 2+2 bodies when the bigger primary is a Roche ellipsoid and the smaller primary is an oblate body

In this problem, one of the primaries of mass m ₁ is a Roche ellipsoid filled with a homogeneous incompressible fluid of density ρ ₁. The smaller primary of mass m ₂ is an oblate body outside the Ellipsoid. The third and the fourth bodies (of mass m ₃ and m ₄ respectively) are small solid spheres of density ρ ₃ and ρ ₄ respectively inside the Ellipsoid, with the assumption that the mass and the radius of the third and the fourth body are infinitesimal. We assume that m ₂ is describing a circle around m ₁. The masses m ₃ and m ₄ mutually attract each other, do not influence the motions of m ₁ and m ₂ but are influenced by them. We have extended the Robe’s restricted three-body problem to 2+2 body problem under the assumption that the fluid body assumes the shape of the Roche ellipsoid (Chandrashekhar in Ellipsoidal figures of equilibrium, Chap. 8, Dover, New York, 1987). We have taken into consideration all the three components of the pressure field in deriving the expression for the buoyancy force viz (i) due to the own gravitational field of the fluid (ii) that originating in the attraction of m ₂ (iii) that arising from the centrifugal force. In this paper, equilibrium solutions of m ₃ and m ₄ and their linear stability are analyzed. We have proved that there exist only six equilibrium solutions of the system, provided they lie within the Roche ellipsoid. In a system where the primaries are considered as Earth-Moon and m ₃,m ₄ as submarines, the equilibrium solutions of m ₃ and m ₄ respectively when the displacement is given in the direction of x ₁-axis or x ₂-axis are unstable.     

Quality Assessment of Atmospheric Motion Vectors Over the Indian Ocean

Because conventional observations over the oceans are not available, especially during tropical cyclones, multi-spectral atmospheric motion vectors (AMVs) estimated from geostationary satellites are routinely assimilated in the numerical weather prediction models at different operational centres across the globe. The derived AMVs are generally validated with radiosonde observations available over land at synoptic hours; however, over the ocean there is a limited scope to assess the quality of AMVs. Over ocean, AMVs can be validated with radiosonde data available from opportunistic ships or using dropsonde data available from aircrafts. In this study, the accuracy of the AMVs derived from the geostationary satellites Kalpana-1 and Meteosat-7 is evaluated over the oceanic region. Radiosonde data available from a ship cruise held in the Bay of Bengal during the period 09 July–08 August 2012 and from the Cal/Val site situated at Kavaratti Island (72.62°E, 10.57°N) in the southern Indian Ocean are used to assess the AMV accuracy. In this study, 83 radiosonde profiles are used to validate the Kalpana-1 AMVs, to allow a better understanding of AMV errors over the Indian Ocean. The RMSVD of Kalpana-1 AMVs for the high-, mid- and low-levels are found to be 7.9, 9.4 and 5.3 m s^?1, respectively, while the corresponding RMSVD for Meteosat-7 AMVs are 9.1, 5.5 and 3.7 m s^?1. A similar accuracy is observed when the AMVs are validated against the NCEP analyses collocated with the nearest radiosonde locations. The high RMSVD and bias for Kalpana-1 AMVs at the mid-level and Meteosat-7 AMVs at the high-level are associated with the limitation of satellite winds to resolve the upper-level easterly jet in conjunction with errors in the height assignment. This study could help the numerical modellers to assign appropriate observation error over this region during the assimilation of AMVs into the NWP models.     

Water chemistry of Mansar Lake (India): an indication of source area weathering and seasonal variability

The chemistry of major elements (Ca, Mg, Na, K and Si) and anions (HCO ₃, SO ₄ and Cl) in the water of Mansar Lake was studied, based on seasonal data. The results show that total dissolved solid (TDS) concentration in a particular season is similar, but varies slightly in different seasons with a variation factor of less than 2. This is because the collections were made in the dry seasons and the Ca-precipitation is the cause for the seasonal variability. The major element chemistry of Mansar Lake is mainly controlled by rock weathering, with HCO ₃ and Ca dominating the major ion composition because of the abundance of carbonate rocks in the basin. The results also indicate that the lake water is saturated with respect to calcite and/or dolomite during the spring season whereas it is undersaturated in the summer season. This contrast brings out seasonal variability. The lake shows disequilibrium with atmospheric CO ₂ as a result of carbonate dissolution in the drainage basin. The study also shows that physical weathering/erosion is dominant and that chemical weathering is incipient. This is consistent with the Chemical Index of Alteration (CIA) data.     

Structural set up in northern part of Kumaun Himalaya

The Main Central Thrust (MCT) and the Main Boundary Thrust (MBT) are the two major thrusts in Kumaun, the MCT forming the boundary between highly sheared, deformed and mylonitized rocks of the Great Himalayan Central Crystallines and the Lesser Himalayan metasedimentaries. While in the Central Crystallines four-folding episodes are observed of which two are of the Precambrian age, the Lesser Himalayan rocks show only two phases of folding. MCT has its own distinctive structural history and the crystalline mass comprises an integral part of peninsular India.     

Origin of trondhjemite and albitite at the expense of A-type granite,Aravalli orogen,India:Evidence from new metasomatic replacement fronts

The A-type Harsora-Dadikar granites in the Alwar complex of northern Aravalli orogen,NW India provide evidence for subsolidus-requilibration of feldspars.They record three new discrete stages of albitisation,producing trondhjemite and albitite sequentially at the expense of original granite.Stage-Ⅰ metasomatism deanorthised the magmatic oligoclase and transformed the grey least-albitised granite to pinkish grey microcline-oligoclase granite.Stage-II converted the latter to trondhjemite by replacement of microcline to oligoclase.Stage-Ⅲ metasomatism led to the formation of albitite/albite granite from trondhjemite,where the metasomatically formed oligoclase was replaced by albite.This stage of metasomatism resulted in nearly complete disappearance of amphibole and biotite,producing a monomineralic rock(albitite),which is consistent with Korzhinskii theory of infiltration metasomatism.The reaction fronts delineating the Stage-Ⅱ and Stage-Ⅲ are sharp and easily discernible by their prominent color differences in Harsora on the outcrop scale.Chemically,the mineral transformations during three stages are manifested by the differential gains/losses in Na,K,Ca,Rb,Ba,Sr,Fe and Mg.The formation of albite,Cl-rich marialitic scapolite and Cl-rich amphibole in the albitised granites are suggestive of Naand Cl-brines as the metasomatising fluids.The fluid-rock interactions,which can significantly transform the pristine mineralogy of granitoids,should be carefully considered to avoid any misinterpretations about their petrological history.     

Nature of magmatism and sedimentation at a Columbia active margin: Insights from combined U–Pb and Lu–Hf isotope data of detrital zircons from NW India

Detrital zircons from a Palaeoproterozoic quartzite, deposited between 1.85 and 1.82 Ga in the northern Aravalli orogen of NW India, show a distinctive age peak of ca. 1.85 Ga and variable, but largely subchondritic εHf_{1.85 Ga} between ? 1.3 and ? 21.0 corresponding to hafnium model ages of 2.5 to 3.6 Ga. These data indicate an important period of reworking of ancient (Eo- to Neoarchaean), strongly heterogeneous continental crust at this time. Prevalence of ca. 1.85 Ga subduction-related granitoids, almost identical U–Pb age spectra and εHf_t of detrital zircons in ca. 1.85 Ga metasedimentary rocks in the Aravalli orogen and the inner Lesser Himalaya indicate similar sediment provenances and thus a geological connection between these two terranes during late Palaeoproterozoic. All together, the data constrain a rapid succession of sedimentation, metamorphism and subduction-related magmatic activity and support the interpretation of an active geodynamic realm along the entire north Indian margin at ca. 1.85 Ga. Comparison of detrital zircon data in conjunction with published paleomagnetic data from north India and other crustal blocks of the Columbia supercontinent, additionally, suggest a close affinity of north India with Madagascar, the Cathaysia block of South China and South Korea during Columbia times.     

Integrated geospatial,geostatistical, and remote-sensing approach to estimate groundwater level in North-western India

The depletion of groundwater resources in Northwest India has been extensively studied. The top priority to meet the scarcity of water for irrigation, industrial and domestic purposes is supplemented by groundwater. Geostatistical modelling approach is considered to be beneficial tool for the assessment, evaluation, monitoring, and management of groundwater resources. This study is an attempt to analyze the spatio-temporal variability of groundwater level in semi-arid region of Panipat district, Haryana, India using kriging technique to fill the data gaps. Ordinary kriging was found optimal for the interpolation of groundwater levels. The results revealed that there was not much seasonal variation and also the groundwater flow direction remained almost constant in the study area during the assessment period. Spatial variability analysis showed significant variation in groundwater level and further depicted that the study area had undergone more or less decline in groundwater over the period of time. To validate the observations and results geo spatial and remote sensing techniques including normalised difference vegetation index and impervious surface relationships were worked out. It was further co-related with the rainfall data and the canal network existing in Panipat region. The integrated approach substantiated the observed results with the ground reality and helped in better understanding of the causes of declining groundwater trend in central part of Panipat.     

Geochemistry of Mansar Lake sediments, Jammu, India: Implication for source-area weathering, provenance, and tectonic setting

The sediment geochemistry, including REE, of surface and core samples from Mansar Lake, along with mineralogical investigations, have been carried out in order to understand the provenance, source area weathering, hydrolic sorting and tectonic setting of the basin. The geochemical signatures preserved in these sediments have been exploited as proxies in order to delineate these different parameters.The major element log values (Fe₂O₃/K₂O) vs (SiO₂/Al₂O₃) and (Na₂O/K₂O) vs (SiO₂/Al₂O₃) demarcate a lithology remarkably similar to that exposed in the catchment area. The chondrite normalized REE patterns of lake samples are similar to Post Archaean Australian Shale (PAAS) with LREE enrichment, a negative Eu anomaly and almost flat HREE pattern similar to a felsic and/or cratonic sedimentary source. However, the La–Th–Sc plot of samples fall in a mixed sedimentary domain, close to Upper Continental Crust (UCC) and PAAS, suggesting sedimentary source rocks for the Mansar detritus. It also indicates that these elements remained immobile during weathering and transportation. The mineralogical characteristic, REEs, and high field strength elements (HFSE), together with the high percentage of metamorphic rock fragments in the Siwalik sandstone, support a metamorphic source for lower Siwalik sediments. A very weak positive correlation between Zr and SiO₂, poor negative correlation with Al₂O₃, negative correlation of (La/Yb)_N and (Gd/Yb)_N ratios with SiO₂ and positive correlation with Al₂O₃, suggest that Zr does not dominantly control the REE distribution in Mansar sediments. The petrographic character and textural immaturity indicate a short distance transport for the detritus. The distribution of elements in core samples reflect fractionation. The higher Zr/Th and Zr/Yb ratios in coarse sediments and PAAS compared to finer grained detritus indicate sedimentary sorting. Plots of the geochemical data on tectonic discrimination diagrams suggest that the sediments derived from the lower Siwalik were originated within a cratonic interior and later deposited along a passive margin basinal setting. It therefore reveals lower Siwalik depositional history.